I don't know what kind of experiment might work like that. The only thing that comes to mind is that it could somehow exploit the superluminal speed of wavefunction collapse to transmit information. But this is, of course, impossible.

Although the collapse itself is instantaneous, it is completely random so there is no information transferred in it. The moment of transfer comes when the two parties use classical communication to compare the measurement results on both parts of the system. But this can never happen faster than with the speed of light.